Low Mass Thermal Dilepton Production at NLO in a Weakly Coupled Quark-Gluon Plasma

TL;DR

This paper computes the NLO production rate of low invariant mass dileptons in a weakly-coupled quark-gluon plasma, providing numerical results and tools for hydrodynamical modeling, with corrections increasing the rate by up to 40%.

Contribution

It extends previous photon rate calculations to include small nonzero invariant mass dileptons at NLO in weakly-coupled thermal QCD, with practical numerical tools.

Findings

NLO corrections increase dilepton rate by 30-40%.

Dilepton measurements can serve as Ersatz photon measurements at high energy.

Provides matching between low and high invariant mass results.

Abstract

We present a computation, within weakly-coupled thermal QCD, of the production rate of low invariant mass ($M^2 \sim g^2 T^2$) dileptons, at next-to-leading order (NLO) in the coupling (which is $O(g^3 e^2 T^2)$). This involves extending the NLO calculation of the photon rate which we recently presented to the case of small nonzero photon invariant mass. Numerical results are discussed and tabulated forms and code are provided for inclusion in hydrodynamical models. We find that NLO corrections can increase the dilepton rate by up to 30-40% relative to leading order. We find that the electromagnetic response of the plasma for real photons and for small invariant mass but high energy dilepton pairs (e.g., $M^2 < (300\:\mathrm{MeV})^2$ but $p_T > 1 \: \mathrm{GeV}$) are close enough that dilepton pair measurements really can serve as Ersatz photon measurements. We also present a matching a la Ghisoiu and Laine between our results and results at larger invariant masses.